Example 1
What is the multiplicity of the roots of y = (x – 1)4(x – 3)7(x + 2)1?
Example 2
y = x4 − 6x3 + 13x2 – 12x + 4 has zeros at 2 and 1. What is their multiplicity?
Example 3
Will f(x) = (x − 21)4(x − 6) go from positive to negative at x = 21 or keep the same sign?
Example 4
Will f(x) = -(x − 9)3(x − 6) go from negative to positive at x = 6 or keep the same sign?
Example 5
A polynomial is even with a positive leading coefficient. Its only real zeros are of even multiplicity. Could the polynomial ever have a y-value of -3?